Search Results for ""

Given a real number x, find the powers of a base b that will shift the digits of x a number of places n to the left. This is equivalent to solving b^x=b^nx (1) or x=n+log_bx. ...

The digraph intersection of two digraphs is the digraph whose vertex set (respectively, edge set) is the intersection of their vertex sets (respectively, edge sets). If n is ...

The Euclidean metric is the function d:R^n×R^n->R that assigns to any two vectors in Euclidean n-space x=(x_1,...,x_n) and y=(y_1,...,y_n) the number ...

Let four lines in a plane represent four roads in general position, and let one traveler T_i be walking along each road at a constant (but not necessarily equal to any other ...

Consider two closed oriented space curves f_1:C_1->R^3 and f_2:C_2->R^3, where C_1 and C_2 are distinct circles, f_1 and f_2 are differentiable C^1 functions, and f_1(C_1) ...

An equilateral parallelogram whose acute angles are 45 degrees. Sometimes, the restriction to 45 degrees is dropped, and it is required only that two opposite angles are ...

Specifying two sides and the angle between them uniquely (up to geometric congruence) determines a triangle. Let c be the base length and h be the height. Then the area is ...

Let L denote the n×n square lattice with wraparound. Call an orientation of L an assignment of a direction to each edge of L, and denote the number of orientations of L such ...

Integrals over the unit square arising in geometric probability are int_0^1int_0^1sqrt(x^2+y^2)dxdy=1/3[sqrt(2)+sinh^(-1)(1)] int_0^1int_0^1sqrt((x-1/2)^2+(y-1/2)^2)dxdy ...

Let there be two particularly well-behaved functions F(x) and p_tau(x). If the limit lim_(tau->0)int_(-infty)^inftyp_tau(x)F(x)dx exists, then p_tau(x) is a regular sequence ...